scholarly journals Crowd behavior dynamics: entropic path-integral model

2009 ◽  
Vol 59 (1-2) ◽  
pp. 351-373 ◽  
Author(s):  
Vladimir G. Ivancevic ◽  
Darryn J. Reid ◽  
Eugene V. Aidman
Keyword(s):  
Path Integral ◽  
Integral Model ◽  
Crowd Behavior ◽  
Behavior Dynamics ◽  
Crowd Behavior Dynamics

GEOMETRICAL AND TOPOLOGICAL DUALITY IN CROWD DYNAMICS

2010 ◽  
Vol 03 (04) ◽  
pp. 493-507 ◽  
Author(s):  
V. G. IVANCEVIC ◽  
D. J. REID
Keyword(s):  
Algebraic Topology ◽  
Duality Theorem ◽  
Geometrical Model ◽  
Related Question ◽  
Crowd Behavior ◽  
Duality Theorems ◽  
Topological Duality ◽  
Crowd Dynamics ◽  
Behavior Dynamics ◽  
Crowd Behavior Dynamics

The purpose of this paper is to establish strong theoretical basis for solving practical problems in modeling the behavior of crowds. Based on the previously developed (entropic) geometrical model of crowd behavior dynamics, in this paper we formulate two duality theorems related to the crowd manifold. Firstly, we formulate the geometrical crowd-duality theorem and prove it using Lie-functorial and Riemannian proofs. Secondly, we formulate the topological crowd-duality theorem and prove it using cohomological and homological proofs. After that we discuss the related question of the connection between Lagrangian and Hamiltonian crowd-duality, and finally establish the globally dual structure of crowd dynamics. All used terms from algebraic topology are defined in Appendix A.

scholarly journals A two-chain path integral model of positronium

2000 ◽  
Vol 113 (23) ◽  
pp. 10642-10650 ◽  
Author(s):  
L. Larrimore ◽  
R. N. McFarland ◽  
P. A. Sterne ◽  
Amy L. R. Bug
Keyword(s):  
Path Integral ◽  
Integral Model

Tunneling as a stochastic process: A path-integral model for microwave experiments

2003 ◽  
Vol 67 (6) ◽  
Author(s):  
A. Ranfagni ◽  
R. Ruggeri ◽  
D. Mugnai ◽  
A. Agresti ◽  
C. Ranfagni ◽  
...  
Keyword(s):  
Stochastic Process ◽  
Path Integral ◽  
Integral Model

scholarly journals PATH INTEGRAL REPRESENTATION FOR INTERFACE STATES OF THE ANISOTROPIC HEISENBERG MODEL

2000 ◽  
Vol 12 (10) ◽  
pp. 1325-1344 ◽  
Author(s):  
OSCAR BOLINA ◽  
PIERLUIGI CONTUCCI ◽  
BRUNO NACHTERGAELE
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Two Dimensions ◽  
Integral Model ◽  
Partition Functions ◽  
Translation Invariant ◽  
Xxz Model ◽  
Path Integral Representation ◽  
Ferromagnetic Chain ◽  
The One

We develop a geometric representation for the ground state of the spin-1/2 quantum XXZ ferromagnetic chain in terms of suitably weighted random walks in a two-dimensional lattice. The path integral model so obtained admits a genuine classical statistical mechanics interpretation with a translation invariant Hamiltonian. This new representation is used to study the interface ground states of the XXZ model. We prove that the probability of having a number of down spins in the up phase decays exponentially with the sum of their distances to the interface plus the square of the number of down spins. As an application of this bound, we prove that the total third component of the spin in a large interval of even length centered on the interface does not fluctuate, i.e. has zero variance. We also show how to construct a path integral representation in higher dimensions and obtain a reduction formula for the partition functions in two dimensions in terms of the partition function of the one-dimensional model.

AN EXACT SOLUBLE PATH INTEGRAL MODEL FOR STOCHASTIC BELTRAMI FLUXES AND ITS STRING PROPERTIES

1999 ◽  
Vol 13 (09n10) ◽  
pp. 317-323 ◽  
Author(s):  
LUIZ C. L. BOTELHO
Keyword(s):  
Surface Structure ◽  
Path Integral ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Reduced Model ◽  
Integral Model ◽  
Vortex Loop ◽  
Random Surface ◽  
Dimensional Space Time ◽  
Three Dimensional Space

We propose an exactly soluble path integral model for stochastic Beltrami fluxes in three-dimensional space-time with a fixed eddie scale. We show further the appearance of a three-dimensional self-avoiding random surface structure for the spatial vortex loop in our exactly soluble turbulence reduced model.

The path integral model of d- pairing superconductors

1996 ◽  
Vol 46 (S2) ◽  
pp. 1041-1042 ◽  
Author(s):  
Peter Brusov ◽  
Natali Brusova ◽  
Paul Brusov
Keyword(s):  
Path Integral ◽  
Integral Model
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